1st Edition

An R Companion to Linear Statistical Models

By Christopher Hay-Jahans Copyright 2012
    372 Pages 97 B/W Illustrations
    by Chapman & Hall

    372 Pages 97 B/W Illustrations
    by Chapman & Hall

    Focusing on user-developed programming, An R Companion to Linear Statistical Models serves two audiences: those who are familiar with the theory and applications of linear statistical models and wish to learn or enhance their skills in R; and those who are enrolled in an R-based course on regression and analysis of variance. For those who have never used R, the book begins with a self-contained introduction to R that lays the foundation for later chapters.

    This book includes extensive and carefully explained examples of how to write programs using the R programming language. These examples cover methods used for linear regression and designed experiments with up to two fixed-effects factors, including blocking variables and covariates. It also demonstrates applications of several pre-packaged functions for complex computational procedures.

    Background
    Getting Started
    Introduction
    Starting up R
    Searching for Help
    Managing Objects in the Workspace
    Installing and Loading Packages from CRAN
    Attaching R Objects
    Saving Graphics Images from R
    Viewing and Saving Session History
    Citing R and Packages from CRAN
    The R Script Editor
    Working with Numbers
    Introduction
    Elementary Operators and Functions
    Sequences of Numbers
    Common Probability Distributions
    User Defined Functions
    Working with Data Structures
    Introduction
    Naming and Initializing Data Structures
    Classifications of Data within Data Structures
    Basics with Univariate Data
    Basics with Multivariate Data
    Descriptive Statistics
    For the Curious
    Basic Plotting Functions
    Introduction
    The Graphics Window
    Boxplots
    Histograms
    Density Histograms and Normal Curves
    Stripcharts
    QQ Normal Probability Plots
    Half-Normal Plots
    Time-Series Plots
    Scatterplots
    Matrix Scatterplots
    Bells and Whistles
    For the Curious
    Automating Flow in Programs
    Introduction
    Logical Variables, Operators, and Statements
    Conditional Statements
    Loops
    Programming Examples
    Some Programming Tips

    Linear Regression Models
    Simple Linear Regression
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Estimating Regression Parameters
    Confidence Intervals for the Mean Response
    Prediction Intervals for New Observations
    For the Curious
    Simple Remedies for Simple Regression
    Introduction
    Improving Fit
    Normalizing Transformations
    Variance Stabilizing Transformations
    Polynomial Regression
    Piecewise Defined Models
    Introducing Categorical Variables
    For the Curious
    Multiple Linear Regression
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Estimating Regression Parameters
    Confidence Intervals for the Mean Response
    Prediction Intervals for New Observations
    For the Curious
    Additional Diagnostics for Multiple Regression
    Introduction
    Detection of Structural Violations
    Diagnosing Multicollinearity
    Variable Selection
    Model Selection Criteria
    For the Curious
    Simple Remedies for Multiple Regression
    Introduction
    Improving Fit
    Normalizing Transformations
    Variance Stabilizing Transformations
    Polynomial Regression
    Adding New Explanatory Variables
    What if None of the Simple Remedies Help?
    For the Curious: Box—Tidwell Revisited

    Linear Models with Fixed-Effects Factors
    One-Factor Models
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Pairwise Comparisons of Treatment Effects
    Testing General Contrasts
    Alternative Variable Coding Schemes
    For the Curious
    One-Factor Models with Covariates
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Pairwise Comparisons of Treatment Effects
    Models with Two or More Covariates
    For the Curious
    One-Factor Models with a Blocking Variable
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Pairwise Comparisons of Treatment Effects
    Tukey’s Nonadditivity Test
    For the Curious
    Two-Factor Models
    Introduction
    Exploratory Data Analysis
    Model Construction and Fit
    Diagnostics
    Pairwise Comparisons of Treatment Effects
    What if Interaction Effects Are Significant?
    Data with Exactly One Observation per Cell
    Two-Factor Models with Covariates
    For the Curious: Scheffe’s F-Tests
    Simple Remedies for Fixed-Effects Models
    Introduction
    Issues with the Error Assumptions
    Missing Variables
    Issues Specific to Covariates
    For the Curious
    Bibliography
    Index

    Biography

    Christopher Hay-Jahans received his Doctor of Arts in mathematics from Idaho State University in 1999. After spending three years at University of South Dakota, he moved to Juneau, Alaska, in 2002 where he has taught a wide range of undergraduate courses at University of Alaska Southeast. Each year, since 2004, he has also been teaching a course on regression and analysis of variance. Students enrolling in this course have included UAS undergraduates, masters and doctoral students from the Juneau Campus of the University of Alaska Fairbanks School of Fisheries and Ocean Sciences, as well as area professionals in the applied sciences. This work was developed as a supplement for his regression and analysis of variance course and is geared to cover topics from a wide range of textbooks, as well as address the interests, needs, and abilities of a fairly diverse group of students.